Suppose that insted of choosing random samples of 25 students from a
population of 100 students, you selected the first 25 students for the
first sample, the next 25 students for the second sample, and so on. How
might this sampling procedure bias the statistical results?

Every Monday a firm sends you a letter correctly predicting the behavior
of a given stock over the coming week. In the 8th letter the firm offers
to sell you more predictions for a fee. You refuse. Why?

A student finds several pairs of triangular numbers that average to a third one, and so
wonders how many more such triples exist — and how to generate
them. With a few inspired variable substitutions and some modular arithmetic, Doctor
Jacques responds, then suggests a few new questions to explore.

I am doing a lab report comparing two different samples of fish. For
the results the teacher wants a t test. What does the t value and
two-tailed p value tell me and how do they compare to each other? Is
this information 'significant' enough to say that variable 2 came from
the same family as variable 1?

I have three employees who have each worked different numbers of days
and learned different numbers of skills in that time. How can I decide
who is the most effective employee by weighting those two factors?

Train cars are loaded with ore. The distribution of ore into the cars
is normally distributed with a mean of 70 tons per car and a standard
deviation of 0.9 tons. What is the probability that the weight of ore
in a randomly selected car will be 70.7 tons or more?

A business struggles to describe its sales performance with an appropriate
measure of central tendency. Doctor Wilko clarifies, using scenarios in
which medians remain unchanged while average sales change -- or the two
move in opposite directions.

What field studies questions like: 1. Take for example that person A has
blonde hair. 2. You know that this person is not famous. 3. You also know
that (10) people know person A. 4. You would like to know that if (10)
people know person A, how many people in a given population also know
someone like person A, someone with blonde hair. 5. You really want to
know how many people with blonde hair there are in a given population
given the answer to #4.

An interesting conversation that defines the general concepts of
average and central tendency, and looks at the usefulness of such
measures both in representing the data and for making predictions
about future events.

I have collected over 120 observations of Internet connection speeds
through my current provider. What is the best way to find an average
of those speeds so I can convince the provider that the service is slow?